Return to airfoil.dem CVS log

Up to [local] / OpenXM_contrib / gnuplot / demo

Annotation of OpenXM_contrib/gnuplot/demo/airfoil.dem, Revision 1.1

1.1     ! maekawa     1: #
        !             2: # $Id: airfoil.dem,v 1.3 1993/10/07 16:53:28 alex Exp $
        !             3: #
        !             4: # This demo shows how to use bezier splines to define NACA four
        !             5: # series airfoils and complex variables to define Joukowski
        !             6: # Airfoils.  It will be expanded after overplotting in implemented
        !             7: # to plot Coefficient of Pressure as well.
        !             8: #              Alex Woo, Dec. 1992
        !             9: #
        !            10: # The definitions below follows: "Bezier presentation of airfoils",
        !            11: # by Wolfgang Boehm, Computer Aided Geometric Design 4 (1987) pp 17-22.
        !            12: #
        !            13: #                              Gershon Elber, Nov. 1992
        !            14: #
        !            15: # m = percent camber
        !            16: # p = percent chord with maximum camber
        !            17: pause 0  "NACA four series airfoils by bezier splines"
        !            18: pause 0  "Will add pressure distribution later with Overplotting"
        !            19: mm = 0.6
        !            20: # NACA6xxx
        !            21: thick = 0.09
        !            22: # nine percent  NACAxx09
        !            23: pp = 0.4
        !            24: # NACAx4xx
        !            25: # Combined this implies NACA6409 airfoil
        !            26: #
        !            27: # Airfoil thickness function.
        !            28: #
        !            29: set xlabel "NACA6409 -- 9% thick, 40% max camber, 6% camber"
        !            30: x0 = 0.0
        !            31: y0 = 0.0
        !            32: x1 = 0.0
        !            33: y1 = 0.18556
        !            34: x2 = 0.03571
        !            35: y2 = 0.34863
        !            36: x3 = 0.10714
        !            37: y3 = 0.48919
        !            38: x4 = 0.21429
        !            39: y4 = 0.58214
        !            40: x5 = 0.35714
        !            41: y5 = 0.55724
        !            42: x6 = 0.53571
        !            43: y6 = 0.44992
        !            44: x7 = 0.75000
        !            45: y7 = 0.30281
        !            46: x8 = 1.00000
        !            47: y8 = 0.01050
        !            48: #
        !            49: # Directly defining the order 8 Bezier basis function for a faster evaluation.
        !            50: #
        !            51: bez_d4_i0(x) =     (1 - x)**4
        !            52: bez_d4_i1(x) = 4 * (1 - x)**3 * x
        !            53: bez_d4_i2(x) = 6 * (1 - x)**2 * x**2
        !            54: bez_d4_i3(x) = 4 * (1 - x)**1 * x**3
        !            55: bez_d4_i4(x) =                  x**4
        !            56:
        !            57: bez_d8_i0(x) =      (1 - x)**8
        !            58: bez_d8_i1(x) =  8 * (1 - x)**7 * x
        !            59: bez_d8_i2(x) = 28 * (1 - x)**6 * x**2
        !            60: bez_d8_i3(x) = 56 * (1 - x)**5 * x**3
        !            61: bez_d8_i4(x) = 70 * (1 - x)**4 * x**4
        !            62: bez_d8_i5(x) = 56 * (1 - x)**3 * x**5
        !            63: bez_d8_i6(x) = 28 * (1 - x)**2 * x**6
        !            64: bez_d8_i7(x) =  8 * (1 - x)    * x**7
        !            65: bez_d8_i8(x) =                   x**8
        !            66:
        !            67:
        !            68: m0 = 0.0
        !            69: m1 = 0.1
        !            70: m2 = 0.1
        !            71: m3 = 0.1
        !            72: m4 = 0.0
        !            73: mean_y(t) = m0 * mm * bez_d4_i0(t) + \
        !            74:            m1 * mm * bez_d4_i1(t) + \
        !            75:            m2 * mm * bez_d4_i2(t) + \
        !            76:            m3 * mm * bez_d4_i3(t) + \
        !            77:            m4 * mm * bez_d4_i4(t)
        !            78:
        !            79: p0 = 0.0
        !            80: p1 = pp / 2
        !            81: p2 = pp
        !            82: p3 = (pp + 1) / 2
        !            83: p4 = 1.0
        !            84: mean_x(t) = p0 * bez_d4_i0(t) + \
        !            85:            p1 * bez_d4_i1(t) + \
        !            86:            p2 * bez_d4_i2(t) + \
        !            87:            p3 * bez_d4_i3(t) + \
        !            88:            p4 * bez_d4_i4(t)
        !            89:
        !            90: z_x(x) = x0 * bez_d8_i0(x) + x1 * bez_d8_i1(x) + x2 * bez_d8_i2(x) + \
        !            91:         x3 * bez_d8_i3(x) + x4 * bez_d8_i4(x) + x5 * bez_d8_i5(x) + \
        !            92:         x6 * bez_d8_i6(x) + x7 * bez_d8_i7(x) + x8 * bez_d8_i8(x)
        !            93:
        !            94: z_y(x, tk) = \
        !            95:    y0 * tk * bez_d8_i0(x) + y1 * tk * bez_d8_i1(x) + y2 * tk * bez_d8_i2(x) + \
        !            96:    y3 * tk * bez_d8_i3(x) + y4 * tk * bez_d8_i4(x) + y5 * tk * bez_d8_i5(x) + \
        !            97:    y6 * tk * bez_d8_i6(x) + y7 * tk * bez_d8_i7(x) + y8 * tk * bez_d8_i8(x)
        !            98:
        !            99: #
        !           100: # Given t value between zero and one, the airfoild curve is defined as
        !           101: #
        !           102: #                      c(t) = mean(t1(t)) +/- z(t2(t)) n(t1(t)),
        !           103: #
        !           104: # where n is the unit normal to the mean line. See the above paper for more.
        !           105: #
        !           106: # Unfortunately, the parametrization of c(t) is not the same for mean(t1)
        !           107: # and z(t2). The mean line (and its normal) can assume linear function t1 = t,
        !           108: #                                                     -1
        !           109: # but the thickness z_y is, in fact, a function of z_x  (t). Since it is
        !           110: # not obvious how to compute this inverse function analytically, we instead
        !           111: # replace t in c(t) equation above by z_x(t) to get:
        !           112: #
        !           113: #                      c(z_x(t)) = mean(z_x(t)) +/- z(t) n(z_x(t)),
        !           114: #
        !           115: # and compute and display this instead. Note we also ignore n(t) and assumes
        !           116: # n(t) is constant in the y direction,
        !           117: #
        !           118:
        !           119: airfoil_y1(t, thick) = mean_y(z_x(t)) + z_y(t, thick)
        !           120: airfoil_y2(t, thick) = mean_y(z_x(t)) - z_y(t, thick)
        !           121: airfoil_y(t) = mean_y(z_x(t))
        !           122: airfoil_x(t) = mean_x(z_x(t))
        !           123: set nogrid
        !           124: set nozero
        !           125: set parametric
        !           126: set xrange [-0.1:1.1]
        !           127: set yrange [-0.1:.7]
        !           128: set trange [ 0.0:1.0]
        !           129: set title "NACA6409 Airfoil"
        !           130: plot airfoil_x(t), airfoil_y(t) title "mean line" w l 2, \
        !           131:      airfoil_x(t), airfoil_y1(t, thick) title "upper surface" w l 1, \
        !           132:      airfoil_x(t), airfoil_y2(t, thick) title "lower surface" w l 1
        !           133: pause -1 "Press Return"
        !           134: mm = 0.0
        !           135: pp = .5
        !           136: thick = .12
        !           137: set title "NACA0012 Airfoil"
        !           138: set xlabel "12% thick, no camber -- classical test case"
        !           139: plot airfoil_x(t), airfoil_y(t) title "mean line" w l 2, \
        !           140:      airfoil_x(t), airfoil_y1(t, thick) title "upper surface" w l 1, \
        !           141:      airfoil_x(t), airfoil_y2(t, thick) title "lower surface" w l 1
        !           142: pause -1 "Press Return"
        !           143: set title ""
        !           144: set xlab ""
        !           145: set key
        !           146: set parametric
        !           147: set samples 100
        !           148: set isosamples 10
        !           149: set data style lines
        !           150: set function style lines
        !           151: pause 0  "Joukowski Airfoil using Complex Variables"
        !           152: set title "Joukowski Airfoil using Complex Variables" 0,0
        !           153: set time
        !           154: set yrange [-.2 : 1.8]
        !           155: set trange [0: 2*pi]
        !           156: set xrange [-.6:.6]
        !           157: zeta(t) = -eps + (a+eps)*exp(t*{0,1})
        !           158: eta(t) = zeta(t) + a*a/zeta(t)
        !           159: eps = 0.06
        !           160: a =.250
        !           161: set xlabel "eps = 0.06 real"
        !           162: plot real(eta(t)),imag(eta(t))
        !           163: pause -1 "Press Return"
        !           164: eps = 0.06*{1,-1}
        !           165: set xlabel "eps = 0.06 + i0.06"
        !           166: plot real(eta(t)),imag(eta(t))
        !           167: pause -1 "Press Return"
        !           168: set title ""
        !           169: set xlabel ""
        !           170: set notime